Endmembers are spectra that are chosen to represent the most “pure” surface materials from which the pixels in a spectral image are composed. Mathematically, they are basis spectra whose physically constrained linear combinations match the pixel spectra (to within some error tolerance), but which themselves cannot be represented by such linear combinations. “Physically constrained” means constrained by positivity, at least. Endmembers that represent radiance spectra must satisfy the positivity constraint. Other physically-based constraints may be imposed, such as sum-to-unity (i.e., the pixels are weighted mixtures of the endmembers) or sum-to-unity or less (i.e., the pixels are weighted mixtures of the endmembers plus “black”). The latter constraint is common for reflectance spectra. The invention allows selection of any of these constraints.
There are two different categories of endmembers and several different methods and algorithms for finding them. The first category consists of endmembers that do not necessarily correspond to specific pixels in the image. For example, they may represent materials of a purer composition than occur in the scene. Such spectra might be obtained from a library of laboratory-measured reflectances for a variety of materials that might be present. Alternatively, the endmembers may represent cluster averages, which match many spectra well but none exactly.
The invention (sometimes termed “SMACC” herein) relates primarily to the second category of endmembers, which are actual pixels in the image. There are several well-known algorithms for finding these endmembers. IDL's ENVI software contains a method based on a “Pixel Purity Index” [ENVI Users Guide, Research Systems, Inc., 2001] and supervised N-dimensional visualization. This method is not automated (it requires manual operation by an analyst) and is fairly time-consuming. Another method, called N-FINDR [http://www.sennacon.com/nfindr/], chooses endmembers based on a maximum-simplex-volume criterion, and is fully automated and reasonably fast.
There are many uses of endmembers, including classification, detection and data compression. The endmembers can be used to identify unique materials in the scene, and thus can be input to classification routines. They can also be used in a constrained least-squares unmixing routine to find targets and their pixel fill fraction, as an alternative to matched filtering. If the number of spectral channels is large, the endmember abundances are sparse (most values are zero), so the abundance image represents an efficient compression of the original data cube. Upon matching the endmembers to library materials, the abundances define the surface material composition of the scene. This enables one to estimate various physical properties, such as surface reflectance at wavelengths not originally measured.